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Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results

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  • W. Briec
  • C. Comes
  • K. Kerstens

    (LEM - Lille - Economie et Management - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

Abstract

The shortage function, an important tool in production theory, measures potential increases in outputs and decreases in inputs for a given direction g at a given date. To develop a temporal version of technical efficiency measurement, we introduce the concept of a temporal shortage function. This temporal efficiency measure is easily computed using linear programming. We also establish a duality result stating that the temporal profit function and the temporal shortage function are dual to one another. This result has two consequences. First, one can derive a shadow price path via the shadow prices of the temporal shortage function. Second, transposing the classic Farrell inefficiency decomposition, temporal profit efficiency is decomposed into temporal technical and temporal allocative efficiency components. Finally, in line with the recent literature on aggregation over firms, this contribution treats the possibilities and limits of the aggregation of efficiency measures over time.
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Suggested Citation

  • W. Briec & C. Comes & K. Kerstens, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," Post-Print hal-00211164, HAL.
    • Handle: RePEc:hal:journl:hal-00211164
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    References listed on IDEAS

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    2. Autant-Bernard, Corinne & Guironnet, Jean-Pascal & Massard, Nadine, 2011. "Agglomeration and social return to R&D: Evidence from French plant productivity changes," International Journal of Production Economics, Elsevier, vol. 132(1), pages 34-42, July.
    3. Kerstens, Kristiaan & Mazza, Paolo & Ren, Tiantian & Van de Woestyne, Ignace, 2022. "Multi-Time and Multi-Moment Nonparametric Frontier-Based Fund Rating: Proposal and Buy-and-Hold Backtesting Strategy," Omega, Elsevier, vol. 113(C).
    4. Emile Blaise Siewe Pougoue & Ibrahim Manu & Innocent Adédédji Labiyi & Thiburce Bokossa, 2019. "Efficacité technique des exploitations avicoles productrices d’œufs au sud du Bénin," Post-Print halshs-01516234, HAL.
    5. Leleu, Hervé & Briec, Walter, 2009. "A DEA estimation of a lower bound for firms' allocative efficiency without information on price data," International Journal of Production Economics, Elsevier, vol. 121(1), pages 203-211, September.
    6. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.
    7. Fu-bao Zhou & Xin-xin Wang & Ying-ke Liu, 2014. "Gas drainage efficiency: an input–output model for evaluating gas drainage projects," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(2), pages 989-1005, November.

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